Random generation of combinatorial structures from a uniform
Theoretical Computer Science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
Random Structures & Algorithms
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-time counting and sampling of two-rowed contingency tables
Theoretical Computer Science
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved bounds for sampling contingency tables
Random Structures & Algorithms
Rapidly Mixing Markov Chains for Sampling Contingency Tables with a Constant Number of Rows
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximate counting by dynamic programming
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Simulated Annealing in Convex Bodies and an 0*(n4) Volume Algorithm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Journal of Computer and System Sciences - STOC 2002
Combinatorics, Probability and Computing
Mathematical aspects of mixing times in Markov chains
Foundations and Trends® in Theoretical Computer Science
Enumerating contingency tables via random permanents
Combinatorics, Probability and Computing
On the Diaconis-Gangolli Markov Chain for Sampling Contingency Tables with Cell-Bounded Entries
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On the Diaconis-Gangolli Markov chain for sampling contingency tables with cell-bounded entries
Journal of Combinatorial Optimization
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We consider the problem of approximately counting integral flows in a network. We show that there is an fpras based on volume estimation if all capacities are sufficiently large, generalising a result of Dyer, Kannan and Mount (1997). We apply this to approximating the number of contingency tables with prescribed cell bounds when the number of rows is constant, but the row sums, column sums and cell bounds may be arbitrary. We provide an fpras for this problem via a combination of dynamic programming and volume estimation. This generalises an algorithm of Cryan and Dyer (2002) for standard contingency tables, but the analysis here is considerably more intricate.